Exploring small-angle emissions in charm quark jets in proton-proton collisions at $\sqrt{s}$ = 5.02 TeV

Using 2017 CMS data from proton-proton collisions at $\sqrt{s}$ = 5.02 TeV, this study measures the angular structure of charm-tagged jets and finds that small-angle emission suppression is consistent with the dead-cone effect in late-$k_\mathrm{T}$ grooming, while similar suppression in soft-drop selections is attributed to large-angle gluon splitting into charm quark-antiquark pairs.

The Gist

The Big Picture: Studying the "Shower" of a Heavy Quark

Imagine you are at a fireworks display. When a single rocket explodes, it sends out a shower of sparks. In the world of particle physics, when high-energy particles collide, they create "jets"—shower-like sprays of smaller particles.

Usually, these sparks come from light particles (like up or down quarks) or massless particles (gluons). But sometimes, the explosion comes from a heavy particle, like a charm quark. Because this particle is heavy, it behaves differently. It's like the difference between a feather floating in the wind and a bowling ball rolling through a crowd. The heavy particle resists changing direction easily.

This paper is about measuring exactly how that "bowling ball" (the charm quark) sprays its sparks compared to the "feathers" (light particles). Specifically, the scientists are looking for a phenomenon called the "dead cone."

What is the "Dead Cone"?

Think of a heavy quark as a person walking through a crowded room.

• Light particles are like people who can easily weave through the crowd, changing direction sharply and often. They spray sparks in all directions, even very close to their path.
• Heavy particles are like the person carrying a large, heavy box. They can't turn sharply. They can't spray sparks too close to their own path because their own weight (mass) pushes back.

This creates a "dead zone" or a dead cone right in front of the heavy particle where no sparks are emitted. The heavier the particle, the wider this empty cone is.

How Did They Measure It?

The scientists used the CMS detector at CERN (a giant machine that smashes protons together). They looked at data from 2017 where protons collided at a specific energy.

To see the "sparks" clearly, they had to filter out the noise. Imagine trying to hear a specific conversation in a loud stadium. You need a way to ignore the crowd noise. They used two different "filters" (algorithms) to clean up the data:

1. The "Late-kT" Filter: This is like looking for the very last, hardest, most direct spark thrown by the heavy particle before it slows down. It focuses on the "core" of the explosion.
2. The "Soft Drop" Filter: This is like looking for the first big spark that breaks away. It catches sparks that are thrown at wider angles.

What Did They Find?

The team compared the "spray patterns" of jets containing a D0 meson (a particle made of a charm quark) against jets that didn't have a heavy quark (inclusive jets).

1. The Shift: They found that the sparks from the heavy charm quark jets were shifted away from the center. Instead of spraying right next to the path (small angles), the sparks were pushed to wider angles.
2. The Dead Cone Confirmed: This shift perfectly matched the prediction of the "dead cone." The heavy charm quark was indeed suppressing the emission of sparks at very small angles, just like the theory predicted.
3. The Two Filters Tell Different Stories:
   • The Late-kT filter showed a clear "dead cone" effect. It was very sensitive to the heavy mass of the charm quark.
   • The Soft Drop filter showed a similar shift, but for a slightly different reason. It seemed to be picking up on instances where a gluon (a force carrier) split into a charm-anticharm pair at a wider angle.

Why Does This Matter?

The paper claims this is the first time they have looked at very high-energy charm jets (over 100 GeV) and successfully isolated this "dead cone" effect while minimizing the messy effects of how particles stick together (hadronization).

Think of it like this: Previous studies were like trying to study the shape of a snowflake while it was melting in your hand. This study managed to look at the snowflake while it was still frozen and sharp, allowing for a much clearer picture of its true structure.

The Bottom Line

The scientists successfully measured the "angular structure" of jets containing charm quarks. They proved that heavy quarks create a "dead cone" where they refuse to emit radiation at small angles. This measurement provides a new, clean reference point for physicists to test their theories about how the strong force works and will serve as a baseline for future experiments involving heavy-ion collisions (where they hope to study how this "dead cone" changes inside the "soup" of the early universe).

In short: They caught a heavy particle in the act of refusing to spray sparks close to its own path, confirming a decades-old prediction about how heavy things move in the quantum world.

Technical Summary

Technical Summary: Exploring Small-Angle Emissions in Charm Quark Jets in Proton-Proton Collisions at $\sqrt{s} = 5.02$ TeV

Problem and Motivation
The formation of jets in high-energy collisions is a multiscale process governed by Quantum Chromodynamics (QCD). While the radiation patterns of light-quark and gluon jets are well understood, heavy-quark jets (specifically charm and bottom) exhibit distinct behaviors due to the quark mass. This mass effectively regularizes infrared and collinear divergences, leading to the "dead-cone effect"—a suppression of gluon emissions within a cone of angle $\theta_d = m_Q/E_Q$ around the emitting heavy quark. Although the dead-cone effect has been directly observed in proton-proton (pp) collisions by the ALICE Collaboration using fully reconstructed $D^0$ mesons, further measurements are required to understand the dependence of final-state radiation on mass scales, particularly at higher transverse momenta ($p_T$) and in regimes suitable for perturbative calculations. Furthermore, characterizing this effect in pp collisions provides a necessary baseline for future studies of medium-induced radiation in heavy-ion collisions, where the dead cone could isolate vacuum emissions from plasma-induced effects.

Methodology
This analysis utilizes proton-proton collision data collected by the CMS experiment at a center-of-mass energy of 5.02 TeV, corresponding to an integrated luminosity of 301 pb$^{-1}$ recorded in 2017. The study focuses on jets with transverse momentum $100 < p_T^{\text{jet}} < 120$ GeV and pseudorapidity $|\eta| < 1.6$.

1. Jet and Meson Reconstruction: Jets are clustered using the anti-$k_T$ algorithm with a radius parameter $R=0.2$. Prompt $D^0$ mesons are identified via their decay into a kaon and a pion ($K\pi$), with candidates required to have $p_T > 4$ GeV and $|y| < 1.2$. Jets containing a $D^0$ candidate within the jet radius are tagged as $D^0$ jets.
2. Jet Grooming and Declustering: To probe the intrajet radiation pattern, jets are reclustered using the Cambridge–Aachen (CA) algorithm. Two grooming strategies are employed to select specific splittings:
   • Late-$k_T$: This algorithm selects the last splitting in the CA declustering tree where the relative transverse momentum $k_T > 1$ GeV. This approach targets hard, collinear emissions, minimizing contributions from hadronization and soft wide-angle radiation.
   • Modified Soft Drop (SD): A standard soft-drop algorithm ($z > z_{\text{cut}}\theta^\beta$ with $z_{\text{cut}}=0.1, \beta=0$) is modified to additionally require $k_T > 1$ GeV. This selects splittings typically at larger angles compared to the late-$k_T$ method.
3. Signal Extraction and Background Subtraction: The prompt $D^0$ signal is extracted from the invariant mass distribution of $K\pi$ pairs using a binned maximum likelihood fit. Non-prompt $D^0$ mesons (originating from $b$-hadron decays) are subtracted using templates derived from the distribution of the distance of closest approach (DCA) significance.
4. Corrections: Measured detector-level distributions are corrected to the stable-particle level. This involves unfolding bin-to-bin migrations using an iterative D'Agostini method, correcting for purity (background), and applying efficiency corrections. The unfolding is validated using PYTHIA8 and HERWIG7 simulations.

Key Contributions

• First Application of Late-$k_T$: This work presents the first application of the late-$k_T$ grooming algorithm to experimental data. It offers a novel method to isolate hard, collinear emissions in heavy-flavor jets, providing a cleaner view of the parton shower compared to traditional grooming.
• High-$p_T$ Charm Jet Substructure: Unlike previous measurements at lower jet $p_T$, this analysis targets jets with $p_T > 100$ GeV. This regime allows for a description within perturbative QCD and accesses dead-cone scales ($m_Q/E_{\text{splitting}}$) that are significantly larger than the scale derived from the total jet energy ($m_Q/p_T^{\text{jet}}$).
• Differential Sensitivity to Gluon Splitting: By comparing the angular distributions obtained from late-$k_T$ and soft-drop grooming, the analysis disentangles the effects of the dead cone from gluon splitting to charm-anticharm pairs ($g \to c\bar{c}$).

Results
The measured angular distributions of splittings for prompt $D^0$ jets are compared to those of inclusive jets and to predictions from PYTHIA8 (CP5 tune) and HERWIG7 (CH3 tune).

• Angular Shift: The splitting-angle distributions for $D^0$ jets are shifted toward larger angles relative to inclusive jets. This shift is consistent with the expectation that the dead-cone effect suppresses emissions at small angles.
• Algorithm Dependence:
  • Late-$k_T$: The suppression of small-angle emissions observed with the late-$k_T$ algorithm is consistent with the dead-cone effect. The contribution from $g \to c\bar{c}$ splittings is found to be negligible in this regime.
  • Soft Drop: The suppression observed with the soft-drop algorithm appears to be induced by $g \to c\bar{c}$ splittings occurring at large angles. The SD algorithm is more sensitive to these large-angle contributions than the late-$k_T$ method.
• Model Comparison: While HERWIG7 describes the inclusive jet angular distribution better than PYTHIA8, neither model fully reproduces the data for prompt $D^0$ jets. Both models predict distributions peaking at larger angles than observed in the data.

Significance
This paper provides the first measurement of charm quark jet substructure for highly energetic jets ($p_T > 100$ GeV) that successfully isolates the hard and collinear region of the jet shower. By minimizing hadronization effects, the measurement enables a more direct connection to perturbative parton shower calculations. The results serve as a critical reference for future studies in heavy-ion collisions, where isolating vacuum emissions (via the dead cone) from medium-induced radiation is essential for understanding the properties of the quark-gluon plasma. The introduction of the late-$k_T$ algorithm in experimental analysis offers a new tool for probing mass effects in QCD radiation patterns.